Extremely hard arithmetic question! Can you solve it?

The sum of 'n' distinct numbers in ascending order is 'k'. It is known that 53 is one of these numbers, and 'a' is the smallest, 79 is the largest. If 53 is taken out, then the rest (n-1) numbers form an arithmetic sequence. The values of n'' and 'a' are given by the equation (n-1)(a+p) = q, where 'p', q'' are constants. Find the numerical values of 'p' and find q'' in terms of k''.